C. Simple Exponential Smoothing
This technique uses a smoothing constant, 𝛼, that has a value between 0 and 1. This
represents the percentage of the forecast error. The formula for the simple exponential smoothing
is:
𝐹𝑡+1= 𝛼 𝑌𝑡 + (1 − 𝛼) 𝐹𝑡
where: 𝐹𝑡+1 = 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑛𝑒𝑥𝑡 𝑝𝑒𝑟𝑖𝑜𝑑
𝑌𝑡 = 𝑎𝑐𝑡𝑢𝑎𝑙 𝑑𝑎𝑡𝑎 𝑜𝑟 𝑑𝑒𝑚𝑎𝑛𝑑 𝑖𝑛 𝑡ℎ𝑒 𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑝𝑒𝑟𝑖𝑜𝑑
𝐹𝑡 = 𝑡ℎ𝑒 𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠𝑙𝑦 𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒𝑑 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑝𝑒𝑟𝑖𝑜𝑑
𝛼 = 𝑎 𝑤𝑒𝑖𝑔ℎ𝑡𝑖𝑛𝑔 𝑓𝑎𝑐𝑡𝑜𝑟 𝑟𝑒𝑓𝑒𝑟𝑟𝑒𝑑 𝑡𝑜 𝑎𝑠 𝑡ℎ𝑒 𝑠𝑚𝑜𝑜𝑡ℎ𝑖𝑛 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
For this method, you will still refer to the Alpha automobile dealer as an example.
Example 3: For this example, you need to compute for the simple exponential smoothing forecast
with a smoothing constant (𝛼 = 0.10).
Month Motorcycles Demanded
January 60
February 70
March 50
April 90
May 10
June 80
July 150
August 70
September 110
October 150
November 130
The formula has a constant variable (1 − 𝛼), therefore (1 − 𝛼) = 0.90, then substitute it
to the exponential smoothing formula.
Your 𝐹𝑡+1 will be 𝐹3 as you are looking for the forecast for the next period (March). Always
start with the third period.
𝑌𝑡 stands for the actual data (demand) in the present period. In this case, your present
period is February (𝑌2 ).
Lastly, 𝐹𝑡 stands for the previously determined forecast for the present period. Since you
are looking for the third period, therefore your present period is 𝐹2 . Take note that you do not
, have any given forecast yet. So, you will get the value of your 𝐹2 from the demand on the first
period (January).
This is a continuous process until 𝐹12 , as the new forecast will be based on the previous
forecast. See below computation for your reference.
Computation for Simple Exponential Smoothing
𝐹3 = 𝛼𝑌2 + (1 − 𝛼) 𝐹2 𝐹8 = 𝛼𝑌7 + (1 − 𝛼) 𝐹7
= (0.10) (70) + (0.90) (60) = (0.10) (150) + (0.90) (59.86)
= 7 + 54 = 15 + 53.87
= 61 = 68.87
𝐹4 = 𝛼𝑌3 + (1 − 𝛼) 𝐹3 𝐹9 = 𝛼𝑌8 + (1 − 𝛼) 𝐹8
= (0.10) (50) + (0.90) (61) = (0.10) (70) + (0.90) (68.87)
= 5 + 54.9 = 7 + 61.98
= 59.9 = 68.98
𝐹5 = 𝛼𝑌4 + (1 − 𝛼) 𝐹4 𝐹10 = 𝛼𝑌9 + (1 − 𝛼) 𝐹9
= (0.10) (90) + (0.90) (59.9) = (0.10) (110) + (0.90) (68.98)
= 9 + 53.91 = 11 + 62.08
= 62.91 = 73.08
𝐹6 = 𝛼𝑌5 + (1 − 𝛼) 𝐹5 𝐹11 = 𝛼𝑌10 + (1 − 𝛼) 𝐹10
= (0.10) (10) + (0.90) (62.91) = (0.10) (150) + (0.90) (73.08)
= 5 + 56.62 = 15 + 65.77
= 57.62 = 80.77
𝐹7 = 𝛼𝑌6 + (1 − 𝛼) 𝐹6 𝐹12 = 𝛼𝑌11 + (1 − 𝛼) 𝐹11
= (0.10) (80) + (0.90) (57.62) = (0.10) (130) + (0.90) (80.77)
= 8 + 51.86 = 13 + 72.69
= 59.86 = 85.69
Table 3. Exponential Smoothing Forecast
Month Demand Forecast
𝛼 = 0.10
January 60 -
February 70 60
March 50 61
April 90 59.9
May 10 62.91
June 80 57.62
July 150 59.86
August 70 68.87
September 110 68.98
October 150 73.08
November 130 80.77
December - 85.69
This technique uses a smoothing constant, 𝛼, that has a value between 0 and 1. This
represents the percentage of the forecast error. The formula for the simple exponential smoothing
is:
𝐹𝑡+1= 𝛼 𝑌𝑡 + (1 − 𝛼) 𝐹𝑡
where: 𝐹𝑡+1 = 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑛𝑒𝑥𝑡 𝑝𝑒𝑟𝑖𝑜𝑑
𝑌𝑡 = 𝑎𝑐𝑡𝑢𝑎𝑙 𝑑𝑎𝑡𝑎 𝑜𝑟 𝑑𝑒𝑚𝑎𝑛𝑑 𝑖𝑛 𝑡ℎ𝑒 𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑝𝑒𝑟𝑖𝑜𝑑
𝐹𝑡 = 𝑡ℎ𝑒 𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠𝑙𝑦 𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒𝑑 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑝𝑒𝑟𝑖𝑜𝑑
𝛼 = 𝑎 𝑤𝑒𝑖𝑔ℎ𝑡𝑖𝑛𝑔 𝑓𝑎𝑐𝑡𝑜𝑟 𝑟𝑒𝑓𝑒𝑟𝑟𝑒𝑑 𝑡𝑜 𝑎𝑠 𝑡ℎ𝑒 𝑠𝑚𝑜𝑜𝑡ℎ𝑖𝑛 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
For this method, you will still refer to the Alpha automobile dealer as an example.
Example 3: For this example, you need to compute for the simple exponential smoothing forecast
with a smoothing constant (𝛼 = 0.10).
Month Motorcycles Demanded
January 60
February 70
March 50
April 90
May 10
June 80
July 150
August 70
September 110
October 150
November 130
The formula has a constant variable (1 − 𝛼), therefore (1 − 𝛼) = 0.90, then substitute it
to the exponential smoothing formula.
Your 𝐹𝑡+1 will be 𝐹3 as you are looking for the forecast for the next period (March). Always
start with the third period.
𝑌𝑡 stands for the actual data (demand) in the present period. In this case, your present
period is February (𝑌2 ).
Lastly, 𝐹𝑡 stands for the previously determined forecast for the present period. Since you
are looking for the third period, therefore your present period is 𝐹2 . Take note that you do not
, have any given forecast yet. So, you will get the value of your 𝐹2 from the demand on the first
period (January).
This is a continuous process until 𝐹12 , as the new forecast will be based on the previous
forecast. See below computation for your reference.
Computation for Simple Exponential Smoothing
𝐹3 = 𝛼𝑌2 + (1 − 𝛼) 𝐹2 𝐹8 = 𝛼𝑌7 + (1 − 𝛼) 𝐹7
= (0.10) (70) + (0.90) (60) = (0.10) (150) + (0.90) (59.86)
= 7 + 54 = 15 + 53.87
= 61 = 68.87
𝐹4 = 𝛼𝑌3 + (1 − 𝛼) 𝐹3 𝐹9 = 𝛼𝑌8 + (1 − 𝛼) 𝐹8
= (0.10) (50) + (0.90) (61) = (0.10) (70) + (0.90) (68.87)
= 5 + 54.9 = 7 + 61.98
= 59.9 = 68.98
𝐹5 = 𝛼𝑌4 + (1 − 𝛼) 𝐹4 𝐹10 = 𝛼𝑌9 + (1 − 𝛼) 𝐹9
= (0.10) (90) + (0.90) (59.9) = (0.10) (110) + (0.90) (68.98)
= 9 + 53.91 = 11 + 62.08
= 62.91 = 73.08
𝐹6 = 𝛼𝑌5 + (1 − 𝛼) 𝐹5 𝐹11 = 𝛼𝑌10 + (1 − 𝛼) 𝐹10
= (0.10) (10) + (0.90) (62.91) = (0.10) (150) + (0.90) (73.08)
= 5 + 56.62 = 15 + 65.77
= 57.62 = 80.77
𝐹7 = 𝛼𝑌6 + (1 − 𝛼) 𝐹6 𝐹12 = 𝛼𝑌11 + (1 − 𝛼) 𝐹11
= (0.10) (80) + (0.90) (57.62) = (0.10) (130) + (0.90) (80.77)
= 8 + 51.86 = 13 + 72.69
= 59.86 = 85.69
Table 3. Exponential Smoothing Forecast
Month Demand Forecast
𝛼 = 0.10
January 60 -
February 70 60
March 50 61
April 90 59.9
May 10 62.91
June 80 57.62
July 150 59.86
August 70 68.87
September 110 68.98
October 150 73.08
November 130 80.77
December - 85.69
